Problem: Compute the sum of all the roots of $(2x+3)(x-4)+(2x+3)(x-6)=0$.
Answer: The quadratic factors as $(2x + 3)(x - 4 + x - 6) = (2x + 3)(2x - 10) = 2(2x + 3)(x - 5).$  Thus, the roots are $-\frac{3}{2}$ and 5, and their sum is $\boxed{\frac{7}{2}}.$